What is the integral of x/((sin(x^2))^2) ?

The integral of x/((sin(x^2))^2) is -1/2 cot(x^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x/((sin(x^2))^2)

\int \frac{x}{( sin ( x ^{2} ) ) ^{2}} d x

- \frac{1}{2} cot (x^{2}) + C

Solution steps

\int \frac{x}{( sin ( x ^{2} ) ) ^{2}} d x

Use the basic trigonometric identity:

\frac{1}{sin ( x )} = csc (x)

= \int x csc^{2} (x^{2}) d x

Apply u-substitution

: \int \frac{csc ^{2} ( u )}{2} d u

= \int \frac{csc ^{2} ( u )}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int csc^{2} (u) d u

Use the common integral:

\int csc^{2} (u) d u = - cot (u)

= \frac{1}{2} (- cot (u))

Substitute back

u = x^{2}

= \frac{1}{2} (- cot (x^{2}))

Simplify

= - \frac{1}{2} cot (x^{2})

Add a constant to the solution

= - \frac{1}{2} cot (x^{2}) + C

\frac{\partial}{\partial x} (y + x cos (t))

\frac{\partial}{\partial x} (tan (2 x + y))

y = \frac{x - 6}{x + 6}

\frac{d}{d x} (\frac{8}{x ^{5}})

(0, 1), (5, - 2)

What is the integral of x/((sin(x^2))^2) ?
The integral of x/((sin(x^2))^2) is -1/2 cot(x^2)+C